You only need the elemental weapon to apply the buff and use the elemental skills, but you can apply the buff on switch and then swap to your ww weapons, only you wont be doing any phys dmg, which really doesn't matter if you 1 hit everything.
I didn't bother to farm TU gear when I was leveling because I was strong enough to get to lvl 90 with only Koth's Lesson maces x 2 and honorific gloves belt boots.